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| Авторизация |
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| Pierce J.F. — Singularity Theory, Rod Theory, And Symmetry Breaking Loads |
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| Предметный указатель |
Action, group 12
Action, group on  spaces 65
Action, group on internal energy function 68
Action, group on load spaces 58 60 62
Action, group, coadjoint 58
Action, group, convective representation 22
Angles (Euler) 11
Antman, S. 2 4 6 68
Betti form 78
Bifurcation problem 85
Bifurcation problem, finite-dimensional 111 115
Bifurcation problem, symmetric 2 116
Bilinear form 45 55 64
Body, constrained 7
Body, material 7
Body, three-dimensional 35
Buzano, E. 2 164
Centerline 7
Centroids 7
Chillingworth, D. 2
Classification Theorem 134
Configuration(s), constrained 28
Configuration(s), constrained, group actions on 30
Configuration(s), constrained, manifold of 28
Configuration(s), equilibrating 84
Configuration(s), equilibrating, orbit of 85
Configuration(s), equilibrating, orbit of, neighborhood of 103
Configuration(s), Kirchhoff theory 9 24
Configuration(s), reference 35
Configuration(s), space of, Kirchhoff theory 9 24
Configuration(s), space of, special Cosserat theory 9 24
Configuration(s), special Cosserat theory 9 24
Configuration(s), straight 3
Configuration(s), three-dimensional 36
Configuration(s), trivial 5 84
Convective (representation), infinitesimal displacements 19 27
Cosserat theory, special, configurations 9 24
Cosserat theory, special, configurations, space of 9 24
Cosserat theory, special, infinitesimal displacements 13 25
Cosserat theory, special, infinitesimal displacements, space of 13 25
Cosserat theory, special, loads 40 63
Cosserat theory, special, loads, representation space 44 63
Crandall, M. 2
Critical point 76
Critical point, constrained 77
Cross section 7
Damon, J. 165
Decomposition theorem 99 100
Decomposition, representation spaces, infinitesimal displacement 78 91
Decomposition, representation spaces, load 80 92
Director (vectors) 7 44
Director (vectors), forces and moments, components of 43
Discriminant 150
Elastica 2
Elastostatic operator, convective representation 75
Elastostatic operator, symmetries 75
Euler angles 11
Euler field (operator) 73
Euler field (operator), convective representation 75
Euler field (operator), linearization 93
Euler field (operator), symmetries 75
Field, Euler 73
Force, three-dimensional, body 36
Force, three-dimensional, constraint 82
Force, three-dimensional, surface 36
Form, Betti 78
Form, bilinear 45 55 62
Form, canonical 132
Form, canonical, classification 13
Form, canonical, oriented 132
Form, canonical, unoriented 132
Function, internal energy 67
Function, internal energy, (in) Kirchhoff theory 68
Function, internal energy, (in) special Cosserat theory 68
Function, internal energy, group action on 68
Function, internal energy, representation 69
Function, potential 71
Function, potential, constrained 76
Function, potential, reduced 110 115
Function, potential, symmetries 72
Geymonat, G. 2
Golubitsky, M. 2 165
Group(s) 11
Group(s), (on) infinitesimal displacements 21
Group(s), (on) infinitesimal displacements, (on) constrained configurations 30
Group(s), (on) infinitesimal displacements, (on) internal energy 61
Group(s), (on) infinitesimal displacements, (on) loads 58
Group(s), action see "Actions"
Group(s), action, (on) configurations 11
Group(s), isotropy 86
Group(s), isotropy, load 83
Group(s), material symmetry 69
Group(s), representations of, convective 22 58
Group(s), representations of, spatial 22 58
Hyperelastic (material) 68
Hypothesis, Kirchhoff 9
Hypothesis, material response 95
Infinitesimal displacements 13 25
Infinitesimal displacements, 3D 36
Infinitesimal displacements, constrained 29
Infinitesimal displacements, representation, convective 19 27
Infinitesimal displacements, representation, spatial 19
Infinitesimal displacements, space of 19 25
Invertibility condition 8
Isotropy, group, configuration 86
Isotropy, group, load 83
Isotropy, group, relations 87
Isotropy, transversal 69
| Kirchhoff (theory) 3
Kirchhoff (theory), configuration 9 24
Kirchhoff (theory), configuration, constrained 28
Kirchhoff (theory), configuration, space of 9 24
Kirchhoff (theory), infinitesimal displacements, convective representation 27
Kirchhoff (theory), infinitesimal displacements, space of 19 25
Load(s), rod, a-priori 33
Load(s), rod, astatic 37
Load(s), rod, astatic, Kirchhoff theory 5
Load(s), rod, astatic, special Cosserat theory 38
Load(s), rod, dead 36 40
Load(s), rod, follower 165
Load(s), rod, live, 3D 59
Load(s), rod, perturbing, canonical form 13
Load(s), rod, perturbing, classification 13
Load(s), rod, perturbing, symmetric 117
Load(s), rod, perturbing, type (class) 134
Load(s), rod, representation space, Kirchhoff theory 54 63
Load(s), rod, representation space, Kirchhoff theory, decomposition of 93
Load(s), rod, representation space, special Cosserat theory 44 63
Load(s), rod, representations of, (as) forces and moments 43
Load(s), rod, representations of, convective 44
Load(s), rod, representations of, spatial 44
Load(s), rod, space of, Kirchhoff theory 54 63
Load(s), rod, space of, Kirchhoff theory, decomposition of 93
Load(s), rod, space of, special Cosserat theory 40 63
Load(s), rod, spaces of, Kirchhoff rod 54
Load(s), rod, spaces of, Kirchhoff rod, decomposition of 89
Load(s), rod, spaces of, special Cosserat theory 63
Load(s), rod, symmetric perturbing 117
Load(s), rod, symmetry-breaking 117
Load(s), rod, systems, dead 34
Load(s), rod, unperturbed 83
Load(s), rod, work done (Kirchhoff theory) 54
Load(s), rod, work done (Kirchhoff theory), convective representation 55
Load(s), rod, work done (Kirchhoff theory), spatial representation 55
Load(s), rod, work done by (special Cosserat theory) 40
Load(s), rod, work done by (special Cosserat theory), (as) forces and moments 42
Load(s), rod, work done by (special Cosserat theory), convective representation 45
Load(s), rod, work done by (special Cosserat theory), spatial representation 45
Load(s), three-dimensional 36
Load(s), three-dimensional, astatic 37
Load(s), three-dimensional, dead 36
Load(s), three-dimensional, work done by 37
Manifold(s), critical 123
Manifold(s), critical, classification of 134
Marsden, J. 2 46
Material body 7
Material cross section 7
Material point 7
Mechanics, symplectic 56
Moments, director components of 42
Morse function 140
Morse theory 140
Multiplication in 25
Multipliers, Lagrange 77 82
Operator, elastostatic 75
Operator, Euler 75
Operator, Euler, linearization 93
Orbit, (of) equilibrating configurations 85
Orbit, trivial 85
Perturbation(s), symmetric 117
Perturbation(s), symmetry-breaking 117
Perturbation(s), type (class) 134
Point, material 7
Poston, T. 2
Problem (rod) 85
Problem (rod), finite dimensional 111 115
Problem (rod), full 2 85 164
Problem (rod), orbit-breaking 1 112
Problem (rod), orbit-breaking, class  146
Problem (rod), orbit-breaking, class  151
Problem (rod), orbit-breaking, class  152
Problem (rod), symmetric buckling 116
Problem (rod), symmetrically perturbed 116 118
Problem (rod), symmetry-breaking 117
Rabinowitz, P. 2
Representation, (of) rod loads, (as) forces and moments 43
Representation, (of) rod loads, convective 44 54
Representation, (of) rod loads, convective, decomposition of 80
Representation, (of) rod loads, spatial 44 54
Representation, infinitesimal displacements, convective 19 27
Representation, infinitesimal displacements, convective, decomposition of 78
Representation, infinitesimal displacements, spatial 19
Representation, space (for), (for) loads,  , Cosserat theory 40 63
Representation, space (for), (for) loads, , decomposition of 80 92
Representation, space (for), (for) loads, , Kirchhoff theory 54 63
Representation, space (for), infinitesimal displacements, Cosserat theory 19 27
Representation, space (for), infinitesimal displacements, decomposition of 78 91
Representation, space (for), infinitesimal displacements, Kirchhoff theory 19 27
Schaeffer, D. 2 165
Simo, J. 46
Space (of), dead loads 36
Space (of), infinitesimal displacements, Kirchhoff theory 19 27
Space (of), infinitesimal displacements, special Cosserat theory 19 27
Space (of), load representation, Kirchhoff theory 54 63
Space (of), load representation, special Cosserat theory 44 64
Space (of), rod loads, Kirchhoff theory 54 63
Space (of), rod loads, special Cosserat theory 40 63
Theorem, classification 134
Theorem, decomposition 99 100
Tubular neighborhood 103
Unfolding 3 120 165
Wan, Y.H. 2
Work, virtual, 64
Work, virtual, (done by) loads, dead, Kirchhoff theory 54 55
Work, virtual, (done by) loads, dead, special Cosserat theory 40 42 45
Work, virtual, three-dimensional 37
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